Question: Multiply the following complex numbers, marked as blue dots on the graph: $(5 e^{3\pi i / 4}) \cdot ( e^{13\pi i / 12})$ (Your current answer will be plotted in orange.)
Answer: Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $5 e^{3\pi i / 4}$ ) has angle $\frac{3}{4}\pi$ and radius $5$ The second number ( $ e^{13\pi i / 12}$ ) has angle $\frac{13}{12}\pi$ and radius $1$ The radius of the result will be $5 \cdot 1$ , which is $5$ The angle of the result is $\frac{3}{4}\pi + \frac{13}{12}\pi = \frac{11}{6}\pi$ The radius of the result is $5$ and the angle of the result is $\frac{11}{6}\pi$.